Turns out they were primed to be knocked off their perch by the crosstown Mets.

Dillon Gee finished off the first Subway Series sweep by the upstarts from Queens, striking out a career-high 12 and limiting the Yankees to four hits over 7 1-3 innings in a 3-1 victory Thursday night that completed the Mets’ four-game smothering of their famous foe from the Bronx.

“It’s hard when you lose to your crosstown rivals,” Yankees manager Joe Girardi said. “You don’t want to be part of a team that gets swept by your crosstown rivals. Over time, it’s going to happen, but you don’t want to be the team that it happens to.”

Marlon Byrd had a two-run, second-deck homer in the second off rookie Vidal Nuno (1-2), John Buck hit a slow-rolling RBI single off third base in the eighth and Gee made that stand up against the Yankees, who were outscored 16-7 in the series and went 5 for 23 (.218) with runners in scoring position.

Thirteen Yankees have made 14 trips to the disabled list that caused them to miss 507 roster days, according to STATS. First baseman Mark Teixeira and third baseman Kevin Youkilis are likely to be activated from the disabled list on Friday, ahead of a weekend series at home against AL East-leading Boston.

“It could be a great boost for us,” Girardi said. “I don’t want to put too much pressure on the guys coming back, but it depends on what kind of starts they get off to.”

Teixeira takes over at first from Lyle Overbay and Youkilis at third from David Adams.

“I don’t want to put too much pressure on the guys coming back, but it depends on what kind of starts they get off to,” Girardi said.

The Yankees could have used them against the Mets. Since the start of interleague play in 1997, the only Subway Series sweep had been a 6-0 whitewash by the Yankees in 2003.

“Does it mean any more that it’s against the Yankees? Had we been playing better, yeah, it would have been huge. But right now we’ve just got to win some games, and it didn’t matter who it was,” Mets manager Terry Collins said. “It establishes a mood in the clubhouse that, you know what, we’re not that bad.”

The Yankees began the week leading the AL East at 30-20. And the Mets, who had never won four straight over the Yankees, were fourth in the NL East at 18-29.

But the Met extended a winning streak to five for the first time since May 5-9 last year. And the Yankees have lost five in a row in a single season for the first time since a six-game slide from May 11-16, 2011.

Using a sharp slider, pinpoint changeup and a fastball in the upper 80s, Gee (3-6) didn’t go to three balls on a single batter, threw 63 of 88 pitches for strikes and retired his final 15 in a row.

“He didn’t get many balls over the middle of the plate,” Gardner said.

Yankees batters, usually patient, have gone three games without a free pass for the first time since June 12-14, 1991, when Kevin Maas was their cleanup hitter.

Gee escaped two-on, no-outs trouble in both the first and second innings, and then allowed just one more runner — on Robinson Cano’s one-out homer in the third, his 14th of the year. Gee and his bullpen retired the Yankees’ last 20 batters.

“Robbie and I took advantage of some pitches to hit in the first inning,” said Gardner. “We didn’t get anything out of it and from there, he had his way with us.”

Scott Rice got the final two outs of the eighth, and Bobby Parnell finished the four-hitter for his ninth save in 11 chances.

Nuno, a 25-year-old left-hander, allowed two runs and three hits in six innings in his third big league start and fifth appearance. Nuno didn’t allow a hit after Anthony Recker’s double in the second and retired his final 10 batters. He appears likely to be sent back to the minor leagues when Pettitte is activated.

“I’m sure there will be a buzz in the air,” Girardi said. “Tomorrow’s as good a day to get back to our winning ways as any.”

NOTES: The game drew 44,207, the second-lowest for a Subway Series game at new Yankee Stadium, ahead of only the 43,681 Wednesday. … The Yankees lost their last four regular-season games in 2011 and their first three in 2012. … The rivals played three games apiece in 1997 and ’98, then six regular-season games a year through 2012. The Yankees brushed past the Mets 4-1 in the 2000 World Series for their third straight title. … Joba Chamberlain, back from a strained oblique, made his first appearance since April 27 and threw a wild pitch before allowing Buck’s single. … The Yankees struck out a season-high 14 times.